Finite Group Databasebeta

← C2×#13072745 #14921356

Subgroups — C2×#13072745 #14921356

Order 2816.

4946 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67000C211yesmaximal, characteristic, complemented
2C22×#66999C211yesmaximal, characteristic, complemented
3C22×#66935C211yesmaximal, characteristic
4C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
5#13072745C2116yesmaximal, direct product factor
6C2×#10622288C211yesmaximal, characteristic, complemented
7C2×#10622285C211yesmaximal, characteristic, complemented
8C2×#10622574C211yesmaximal, characteristic, complemented
9C2×#10622570C211yesmaximal, characteristic, complemented
10C2×#10622558C211yesmaximal, characteristic, complemented
11C2×#10622283C211yesmaximal, characteristic, complemented
12C2×#10622278C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic, complemented
14C2×#10622568C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#393C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×Q8×C11C2211yescharacteristic, complemented
19C23×C22⋊D11C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×D44C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C2×#67000—28no—
30C2×#67000C2218yescomplemented
31C2×#66999—28no—
32C2×#66999C2218yescomplemented
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
42C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
43C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
44C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
45C22×C4⋊Dic11C2211yescharacteristic, complemented
46C22×Dic11⋊C4C2211yescharacteristic, complemented
47C22×Dic11⋊C4C2211yescharacteristic, complemented
48C22×C4×Dic11C2211yescharacteristic, complemented
49C22×C4×Dic11C2211yescharacteristic, complemented
50C2×#66935—28no—
51C2×#66935C2218yes—
52C2×C22⋊C4×D11—28no—
53C2×C22⋊C4×D11C2218yescomplemented
54C11×#393C2218yescomplemented
55C2×C11×#95C2211yescharacteristic, complemented
56C2×C11×#95C2211yescharacteristic, complemented
57C2×C11×#95C2211yescharacteristic, complemented
58C2×C11⋊#95C2211yescharacteristic, complemented
59C2×C11⋊#95C2211yescharacteristic, complemented
60C2×C11⋊#95C2211yescharacteristic, complemented
61#10622574C2218yescomplemented
62#10622570C2218yescomplemented
63#10622568C2218yescomplemented
64#10622558C2218yescomplemented
65#10622288C2218yescomplemented
66#10622285C2218yescomplemented
67#10622283C2218yescomplemented
68#10622279C2218yescomplemented
69#10622278C2218yescomplemented
70#10622278C2218yescomplemented
71C25×C11C2311yescharacteristic
72C24×D11—24no—
73C24×D11—24no—
74C24×D11—24no—
75C24×D11—24no—
76C24×D11—24no—
77C24×D11—42no—
78C24×D11—42no—
79C24×D11C2311yescharacteristic
80C24×D11C2311yescharacteristic
81C24×D11C2314yes—
82C24×D11C2311yescharacteristic
83C22×Q8×C11—24no—
84C22×Q8×C11—24no—
85C22×Q8×C11—42no—
86C22×Q8×C11C2314yescomplemented
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C22×C22⋊D11—24no—
94C22×C22⋊D11—24no—
95C22×C22⋊D11—42no—
96C22×C22⋊D11C2314yes—
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C22×D44—24no—
103C22×D44—24no—
104C22×D44—24no—
105C22×D44—24no—
106C22×D44—24no—
107C22×D44—42no—
108C22×D44C2314yes—
109C22×D44C2314yes—
110C22×C4×D11—24no—
111C22×C4×D11—24no—
112C22×C4×D11—24no—
113C22×C4×D11—24no—
114C22×C4×D11—42no—
115C22×C4×D11—42no—
116C22×C4×D11C2314yes—
117C22×C4×D11C2314yes—
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4—24no—
120C2×C11×C22⋊C4—42no—
121C2×C11×C22⋊C4C2314yes—
122C2×C11×C22⋊C4C2314yes—
123C2×C11×C22⋊C4C2314yes—
124C2×C22⋊Dic11—24no—
125C2×C22⋊Dic11—24no—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128#67000—232no—
129#66999—232no—
130C2×(C2×D11)⋊C4—24no—
131C2×(C2×D11)⋊C4—24no—
132C2×(C2×D11)⋊C4—24no—
133C2×(C2×D11)⋊C4—24no—
134C2×(C2×D11)⋊C4—24no—
135C2×(C2×D11)⋊C4—24no—
136C2×(C2×D11)⋊C4—24no—
137C2×(C2×D11)⋊C4—42no—
138C2×(C2×D11)⋊C4—42no—
139C2×(C2×D11)⋊C4—42no—
140C2×(C2×D11)⋊C4D418yes—
141C2×(C2×D11)⋊C4D418yescomplemented
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×(C2×D11)⋊C4C2314yes—
148C2×(C2×D11)⋊C4C2314yes—
149C2×(C2×D11)⋊C4C2314yes—
150C2×(C2×D11)⋊C4C2314yescomplemented
151C2×(C2×D11)⋊C4C2314yescomplemented
152C2×(C2×D11)⋊C4C2314yescomplemented
153C2×(C2×D11)⋊C4C2314yescomplemented
154C2×C4⋊Dic11—24no—
155C2×C4⋊Dic11C2314yescomplemented
156C2×Dic11⋊C4—24no—
157C2×Dic11⋊C4—24no—
158C2×Dic11⋊C4C2314yescomplemented
159C2×Dic11⋊C4C2314yescomplemented
160C2×C4×Dic11—24no—
161C2×C4×Dic11—42no—
162C2×C4×Dic11C2314yescomplemented
163C2×C4×Dic11C2314yescomplemented
164#66935—232no—
165C22⋊C4×D11—232no—
166C11×#95C2314yescomplemented
167C11×#95C2314yescomplemented
168C11×#95C2314yescomplemented
169C11⋊#95C2314yescomplemented
170C11⋊#95C2314yescomplemented
171C11⋊#95C2314yescomplemented
172C2×#2472—111nomaximal, Sylow
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11#4114yes—
180C24×C11C2412yes—
181C24×C11C2411yescharacteristic
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—232no—
187C23×D11—22no—
188C23×D11—28no—
189C23×D11—22no—
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—28no—
195C23×D11—28no—
196C23×D11—22no—
197C23×D11—22no—
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—22no—
201C23×D11—22no—
202C23×D11—22no—
203C23×D11—28no—
204C23×D11—28no—
205C23×D11—44no—
206C23×D11—44no—
207C23×D11—416no—
208C23×D11—416no—
209C23×D11—416no—
210C23×D11—416no—
211C23×D11—416no—
212C23×D11—416no—
213C23×D11C2×D414yes—
214C23×D11C2×D414yes—
215C23×D11#4114yes—
216C23×D11#4114yes—
217C23×D11C2412yes—
218C23×D11C2412yes—
219C23×D11C2412yes—
220C2×Q8×C11—28no—
221C2×Q8×C11—28no—
222C2×Q8×C11—44no—
223C2×Q8×C11—416no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11—22no—
231C22×C4×C11—22no—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11—22no—
235C22×C4×C11—22no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—22no—
239C22×C4×C11—22no—
240C22×C4×C11C2×D414yes—
241C22×C4×C11C2×D414yes—
242C22×C4×C11C2412yes—
243C22×C4×C11C2412yes—
244C22×C4×C11C2412yes—
245C22×C4×C11C2412yes—
246C22×C4×C11C2412yes—
247C22×C4×C11C2412yes—
248C2×C22⋊D11—28no—
249C2×C22⋊D11—28no—
250C2×C22⋊D11—44no—
251C2×C22⋊D11—416no—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—22no—
255C22×Dic11—22no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11—22no—
259C22×Dic11—22no—
260C22×Dic11—22no—
261C22×Dic11—22no—
262C22×Dic11—22no—
263C22×Dic11—22no—
264C22×Dic11—22no—
265C22×Dic11C2×D414yes—
266C22×Dic11C2×D414yes—
267C22×Dic11C2412yes—
268C22×Dic11C2412yes—
269C22×Dic11C2412yes—
270C22×Dic11C2412yes—
271C22×Dic11C2412yes—
272C2×D44—28no—
273C2×D44—28no—
274C2×D44—28no—
275C2×D44—28no—
276C2×D44—28no—
277C2×D44—44no—
278C2×D44—416no—
279C2×D44—416no—
280C2×C4×D11—28no—
281C2×C4×D11—28no—
282C2×C4×D11—28no—
283C2×C4×D11—28no—
284C2×C4×D11—44no—
285C2×C4×D11—44no—
286C2×C4×D11—416no—
287C2×C4×D11—416no—
288C11×C22⋊C4—28no—
289C11×C22⋊C4—28no—
290C11×C22⋊C4—44no—
291C22⋊Dic11—28no—
292C22⋊Dic11—28no—
293(C2×D11)⋊C4—28no—
294(C2×D11)⋊C4—28no—
295(C2×D11)⋊C4—28no—
296(C2×D11)⋊C4—28no—
297(C2×D11)⋊C4—28no—
298(C2×D11)⋊C4—28no—
299(C2×D11)⋊C4—28no—
300(C2×D11)⋊C4—44no—
301(C2×D11)⋊C4—44no—
302(C2×D11)⋊C4—44no—
303(C2×D11)⋊C4C2×D4116yes—
304(C2×D11)⋊C4C2×D4116yescomplemented
305C4⋊Dic11—28no—
306Dic11⋊C4—28no—
307Dic11⋊C4—28no—
308C4×Dic11—28no—
309C4×Dic11—44no—
310C22×#124—111no—
311C22×C22⋊Q8—111no—
312C22×#120—111no—
313C23×C22⋊C4—111no—
314#2472—1116no—
315C2×#397—111no—
316C2×#394—111no—
317C2×#394—111no—
318C2×#393D1111yescharacteristic, complemented
319C2×#390—111no—
320C2×#388—111no—
321C2×#388—111no—
322C2×#386—111no—
323C2×#386—111no—
324C2×#379—111no—
325C2×C4×C22⋊C4—111no—
326C23×C11—28no—
327C23×C11—28no—
328C23×C11—28no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—44no—
336C23×C11—44no—
337C23×C11—44no—
338C23×C11—44no—
339C23×C11C22×D412yes—
340C23×C11C22×D412yes—
341C23×C11C2×#4114yes—
342C23×C11C2×#4112yes—
343C23×C11C2×#4112yes—
344C23×C11C2×#4112yes—
345C23×C11H(5,𝔽2)12yes—
346C23×C11H(5,𝔽2)12yes—
347C23×C11C2511yescharacteristic
348C22×D11—28no—
349C22×D11—28no—
350C22×D11—28no—
351C22×D11—28no—
352C22×D11—28no—
353C22×D11—28no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—232no—
359C22×D11—28no—
360C22×D11—28no—
361C22×D11—28no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—416no—
376C22×D11—416no—
377C22×D11—416no—
378C22×D11—416no—
379C22×D11—416no—
380C22×D11—4128no—
381C22×D11—44no—
382C22×D11—44no—
383C22×D11—44no—
384C22×D11—44no—
385C22×D11—416no—
386C22×D11—44no—
387C22×D11—44no—
388C22×D11—44no—
389C22×D11—44no—
390C22×D11—44no—
391C22×D11—44no—
392C22×D11—44no—
393C22×D11#124116yescomplemented
394C22×D11C22×D414yes—
395C22×D11C22×D414yes—
396C22×D11C2×#4114yes—
397C22×D11C2×#4114yes—
398Q8×C11—416no—
399C2×C4×C11—28no—
400C2×C4×C11—28no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—44no—
418C2×C4×C11—44no—
419C2×C4×C11—44no—
420C2×C4×C11—44no—
421C2×C4×C11C22×D414yes—
422C2×C4×C11C22×D414yes—
423C22⋊D11—416no—
424C2×Dic11—28no—
425C2×Dic11—28no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—44no—
440C2×Dic11—44no—
441C2×Dic11—44no—
442C2×Dic11C22×D414yes—
443C2×Dic11C22×D414yes—
444D44—416no—
445D44—416no—
446C4×D11—416no—
447C4×D11—416no—
448C26—111no—
449C23×Q8C2×D1111yescharacteristic, complemented
450C23×D4—111no—
451C23×D4—111no—
452C23×D4—111no—
453C24×C4—111no—
454C24×C4—111no—
455C2×#124—118no—
456C2×#124—228no—
457C2×C22⋊Q8—118no—
458C2×C22⋊Q8—228no—
459C2×#120—118no—
460C2×#120—228no—
461C22×C4⋊C4—111no—
462C22×C4⋊C4—111no—
463C22×C4⋊C4—111no—
464C22×C22⋊C4—111no—
465C22×C22⋊C4—111no—
466C22×C22⋊C4—111no—
467C22×C22⋊C4—111no—
468C22×C22⋊C4—111no—
469C22×C22⋊C4—111no—
470C22×C22⋊C4—111no—
471C22×C22⋊C4—111no—
472C22×C22⋊C4—111no—
473C22×C22⋊C4—111no—
474C22×C22⋊C4—111no—
475C22×C22⋊C4—111no—
476C22×C22⋊C4—111no—
477C22×C22⋊C4—111no—
478C22×C22⋊C4—118no—
479C22×C22⋊C4—228no—
480C22×C22⋊C4C2×D1111yescharacteristic
481C22×C22⋊C4C2×D1111yescharacteristic
482C22×C22⋊C4C2×D1111yescharacteristic
483C22×C42—111no—
484C22×C42—111no—
485#397—118no—
486#394—118no—
487#394—118no—
488#393C2×D1118yescomplemented
489#390—118no—
490#388—118no—
491#388—118no—
492#386—118no—
493#386—118no—
494#379—118no—
495C4×C22⋊C4—118no—
496C2×#95—111no—
497C2×#95—111no—
498C2×#95—111no—
499C2×#95C2×D1111yescharacteristic, complemented
500C2×#95C2×D1111yescharacteristic, complemented
501C2×#95C2×D1111yescharacteristic, complemented
502C22×C11—24no—
503C22×C11—24no—
504C22×C11—24no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—42no—
509C22×C11—416no—
510C22×C11#52514yes—
511C22×C11C2×#12414yes—
512C22×C11#53814yes—
513C22×C11D4214yes—
514C22×C11#54614yes—
515C22×C11#54614yes—
516C22×C11#55114yes—
517C22×C11C23×D411yescharacteristic
518C22×C11C23×D411yescharacteristic
519C22×C11C22×#4111yescharacteristic
520C22×C11C22×#4111yescharacteristic
521C22×C11C22×#4111yescharacteristic
522C22×C11C2×H(5,𝔽2)11yescharacteristic
523C22×C11C2×H(5,𝔽2)11yescharacteristic
524C2×D11—24no—
525C2×D11—24no—
526C2×D11—24no—
527C2×D11—24no—
528C2×D11—24no—
529C2×D11—24no—
530C2×D11—232no—
531C2×D11—24no—
532C2×D11—24no—
533C2×D11—24no—
534C2×D11—464no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—416no—
540C2×D11—42no—
541C2×D11—42no—
542C2×D11—42no—
543C2×D11—42no—
544C2×D11—42no—
545C2×D11—42no—
546C2×D11—42no—
547C2×D11—88no—
548C2×D11C2×#12418yescomplemented
549C4×C11—24no—
550C4×C11—24no—
551C4×C11—42no—
552C4×C11—42no—
553C4×C11—42no—
554C4×C11—42no—
555Dic11—24no—
556Dic11—24no—
557Dic11—42no—
558Dic11—42no—
559Dic11—42no—
560C25—111no—
561C25—111no—
562C25—111no—
563C25—114no—
564C25—224no—
565C25—224no—
566C25—224no—
567C25—224no—
568C25—224no—
569C25—442no—
570C25—442no—
571C25C22×D1111yescharacteristic
572C22×Q8—24no—
573C22×Q8—24no—
574C22×Q8—42no—
575C22×Q8C22×D1114yescomplemented
576C22×D4—114no—
577C22×D4—114no—
578C22×D4—114no—
579C22×D4—224no—
580C22×D4—224no—
581C22×D4—224no—
582C22×D4—224no—
583C22×D4—224no—
584C22×D4—224no—
585C22×D4—224no—
586C22×D4—442no—
587C22×D4—442no—
588C23×C4—111no—
589C23×C4—111no—
590C23×C4—111no—
591C23×C4—111no—
592C23×C4—111no—
593C23×C4—114no—
594C23×C4—114no—
595C23×C4—224no—
596C23×C4—224no—
597C23×C4—224no—
598C23×C4—224no—
599C23×C4—442no—
600C23×C4—442no—
601C23×C4C22×D1111yescharacteristic
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1111yescharacteristic
604C23×C4C22×D1111yescharacteristic
605C23×C4C22×D1111yescharacteristic
606C23×C4C22×D1111yescharacteristic
607#124—2232no—
608C22⋊Q8—2232no—
609#120—2232no—
610C2×C4⋊C4—114no—
611C2×C4⋊C4—114no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4—224no—
614C2×C4⋊C4—224no—
615C2×C4⋊C4—224no—
616C2×C22⋊C4—24no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—42no—
619C2×C22⋊C4—118no—
620C2×C22⋊C4—118no—
621C2×C22⋊C4—114no—
622C2×C22⋊C4—114no—
623C2×C22⋊C4—114no—
624C2×C22⋊C4—114no—
625C2×C22⋊C4—114no—
626C2×C22⋊C4—114no—
627C2×C22⋊C4—114no—
628C2×C22⋊C4—114no—
629C2×C22⋊C4—114no—
630C2×C22⋊C4—114no—
631C2×C22⋊C4—114no—
632C2×C22⋊C4—114no—
633C2×C22⋊C4—114no—
634C2×C22⋊C4—114no—
635C2×C22⋊C4—2232no—
636C2×C22⋊C4—224no—
637C2×C22⋊C4—224no—
638C2×C22⋊C4—224no—
639C2×C22⋊C4—224no—
640C2×C22⋊C4—224no—
641C2×C22⋊C4—224no—
642C2×C22⋊C4—224no—
643C2×C22⋊C4—224no—
644C2×C22⋊C4—224no—
645C2×C22⋊C4—442no—
646C2×C22⋊C4—442no—
647C2×C22⋊C4—442no—
648C2×C22⋊C4C22×D1114yes—
649C2×C22⋊C4C22×D1114yes—
650C2×C22⋊C4C22×D1114yes—
651C2×C42—114no—
652C2×C42—114no—
653C2×C42—224no—
654C2×C42—442no—
655#95—114no—
656#95—114no—
657#95—114no—
658#95C22×D1114yescomplemented
659#95C22×D1114yescomplemented
660#95C22×D1114yescomplemented
661C2×C11—44no—
662C2×C11#247218yescomplemented
663C2×C11C2×#52511yescharacteristic
664C2×C11C22×#12411yescharacteristic
665C2×C11C2×#53811yescharacteristic
666C2×C11C2×D4211yescharacteristic
667C2×C11C2×#54611yescharacteristic
668C2×C11C2×#54611yescharacteristic
669C2×C11C2×#55111yescharacteristic
670D11—28no—
671D11—44no—
672D11—82no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—114no—
680C24—114no—
681C24—114no—
682C24—112no—
683C24—114no—
684C24—112no—
685C24—112no—
686C24—228no—
687C24—228no—
688C24—228no—
689C24—228no—
690C24—2232no—
691C24—222no—
692C24—222no—
693C24—222no—
694C24—222no—
695C24—222no—
696C24—222no—
697C24—228no—
698C24—222no—
699C24—222no—
700C24—222no—
701C24—222no—
702C24—222no—
703C24—222no—
704C24—222no—
705C24—222no—
706C24—222no—
707C24—222no—
708C24—222no—
709C24—444no—
710C24—444no—
711C24—4416no—
712C24—4416no—
713C24—4416no—
714C24—4416no—
715C24—4416no—
716C24—4416no—
717C24#434314yes—
718C24C23×D1112yes—
719C24C23×D1111yescharacteristic
720C2×Q8—28no—
721C2×Q8—28no—
722C2×Q8—44no—
723C2×Q8—416no—
724C2×D4—228no—
725C2×D4—228no—
726C2×D4—228no—
727C2×D4—228no—
728C2×D4—228no—
729C2×D4—228no—
730C2×D4—228no—
731C2×D4—444no—
732C2×D4—4416no—
733C2×D4—4416no—
734C2×D4—444no—
735C2×D4—4416no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—114no—
753C22×C4—114no—
754C22×C4—112no—
755C22×C4—112no—
756C22×C4—112no—
757C22×C4—112no—
758C22×C4—112no—
759C22×C4—228no—
760C22×C4—228no—
761C22×C4—228no—
762C22×C4—222no—
763C22×C4—222no—
764C22×C4—222no—
765C22×C4—222no—
766C22×C4—222no—
767C22×C4—222no—
768C22×C4—222no—
769C22×C4—222no—
770C22×C4—222no—
771C22×C4—222no—
772C22×C4—222no—
773C22×C4—222no—
774C22×C4—222no—
775C22×C4—228no—
776C22×C4—444no—
777C22×C4—444no—
778C22×C4—4416no—
779C22×C4—4416no—
780C22×C4D4×D1114yes—
781C22×C4D4×D1114yes—
782C22×C4C23×D1112yes—
783C22×C4C23×D1112yes—
784C22×C4C23×D1112yes—
785C22×C4C23×D1112yes—
786C22×C4C23×D1112yes—
787C22×C4C23×D1112yes—
788C4⋊C4—228no—
789C4⋊C4—228no—
790C4⋊C4—228no—
791C22⋊C4—28no—
792C22⋊C4—28no—
793C22⋊C4—44no—
794C22⋊C4—1116no—
795C22⋊C4—1116no—
796C22⋊C4—228no—
797C22⋊C4—228no—
798C22⋊C4—228no—
799C22⋊C4—228no—
800C22⋊C4—228no—
801C22⋊C4—228no—
802C22⋊C4—228no—
803C22⋊C4—228no—
804C22⋊C4—228no—
805C22⋊C4—444no—
806C22⋊C4—444no—
807C22⋊C4—444no—
808C42—228no—
809C42—444no—
810C11C2×#247211yescharacteristic, complemented, Sylow
811C23—28no—
812C23—28no—
813C23—28no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—44no—
821C23—44no—
822C23—44no—
823C23—44no—
824C23—114no—
825C23—114no—
826C23—114no—
827C23—1116no—
828C23—114no—
829C23—2232no—
830C23—228no—
831C23—228no—
832C23—228no—
833C23—228no—
834C23—222no—
835C23—222no—
836C23—222no—
837C23—222no—
838C23—228no—
839C23—228no—
840C23—228no—
841C23—228no—
842C23—222no—
843C23—222no—
844C23—222no—
845C23—222no—
846C23—222no—
847C23—222no—
848C23—228no—
849C23—222no—
850C23—222no—
851C23—222no—
852C23—222no—
853C23—222no—
854C23—222no—
855C23—222no—
856C23—4416no—
857C23—4416no—
858C23—4416no—
859C23—4416no—
860C23—4416no—
861C23—4416no—
862C23—44128no—
863C23—444no—
864C23—444no—
865C23—444no—
866C23—444no—
867C23—444no—
868C23—444no—
869C23—444no—
870C23—444no—
871C23—444no—
872C23—444no—
873C23—444no—
874C23C2×D4×D1112yes—
875C23C2×D4×D1112yes—
876C23#6703712yes—
877C23C2×#434314yes—
878C23C2×#434312yes—
879C23#41×D1112yes—
880C23#41×D1112yes—
881C23#6704212yes—
882C23C24×D1111yescharacteristic
883Q8—416no—
884D4—4416no—
885D4—4416no—
886D4—4416no—
887C2×C4—28no—
888C2×C4—28no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—44no—
906C2×C4—44no—
907C2×C4—44no—
908C2×C4—44no—
909C2×C4—114no—
910C2×C4—114no—
911C2×C4—228no—
912C2×C4—222no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—228no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—222no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—222no—
926C2×C4—4416no—
927C2×C4—4416no—
928C2×C4—444no—
929C2×C4—444no—
930C2×C4—444no—
931C2×C4C2×D4×D1114yes—
932C2×C4C2×D4×D1114yes—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—42no—
937C22—42no—
938C22—416no—
939C22—42no—
940C22—42no—
941C22—118no—
942C22—224no—
943C22—224no—
944C22—224no—
945C22—2232no—
946C22—224no—
947C22—224no—
948C22—224no—
949C22—224no—
950C22—224no—
951C22—224no—
952C22—4464no—
953C22—442no—
954C22—442no—
955C22—442no—
956C22—4416no—
957C22—442no—
958C22—442no—
959C22—442no—
960C22—442no—
961C22—442no—
962C22—442no—
963C22—442no—
964C22—442no—
965C22—888no—
966C22#1062312114yes—
967C22#1062315814yes—
968C22#1062316114yes—
969C22#1062316814yes—
970C22D11×#12414yes—
971C22#1062320714yes—
972C22#1062320914yes—
973C22C22×D4×D1111yescharacteristic
974C22C22×D4×D1111yescharacteristic
975C22C2×#6703711yescharacteristic
976C22C22×#434311yescharacteristic
977C22C2×#41×D1111yescharacteristic
978C22C2×#41×D1111yescharacteristic
979C22C2×#6704211yescharacteristic
980C4—24no—
981C4—24no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—224no—
987C4—224no—
988C4—442no—
989C4—442no—
990C4—442no—
991C2—44no—
992C2—228no—
993C2—444no—
994C2—882no—
995C2#1307274518yesdirect product factor
996C2C2×#1062315811yescharacteristic
997C2C2×D11×#12411yescharacteristic
998C2C2×#1062320911yescharacteristic
999C2C2×#1062312111yescharacteristic
1000C2C2×#1062316111yescharacteristic
1001C2C2×#1062320711yescharacteristic
1002C2C2×#1062316811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#393C2
socleC24×C11C24
prime radicalC22×#66935C2
hypercenterC2×#393D11
hypocenterC11C2×#2472
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#393

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#67000C2semidirect
2. C22×#66999C2semidirect
4. C22×C22⋊C4×D11C2semidirect
5. #13072745C2direct (N × H)
6. C2×#10622288C2semidirect
7. C2×#10622285C2semidirect
8. C2×#10622574C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622558C2semidirect
11. C2×#10622283C2semidirect
12. C2×#10622278C2semidirect
13. C2×#10622278C2semidirect
14. C2×#10622568C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#393C2semidirect
18. C23×Q8×C11C22semidirect
30. C2×#67000C22semidirect
32. C2×#66999C22semidirect
41. C22×(C2×D11)⋊C4C22semidirect
42. C22×(C2×D11)⋊C4C22semidirect
43. C22×(C2×D11)⋊C4C22semidirect
44. C22×(C2×D11)⋊C4C22semidirect
45. C22×C4⋊Dic11C22semidirect
46. C22×Dic11⋊C4C22semidirect
47. C22×Dic11⋊C4C22semidirect
48. C22×C4×Dic11C22semidirect
49. C22×C4×Dic11C22semidirect
53. C2×C22⋊C4×D11C22semidirect
54. C11×#393C22semidirect
55. C2×C11×#95C22semidirect
56. C2×C11×#95C22semidirect
57. C2×C11×#95C22semidirect
58. C2×C11⋊#95C22semidirect
59. C2×C11⋊#95C22semidirect
60. C2×C11⋊#95C22semidirect
61. #10622574C22semidirect
62. #10622570C22semidirect
63. #10622568C22semidirect
64. #10622558C22semidirect
65. #10622288C22semidirect
66. #10622285C22semidirect
67. #10622283C22semidirect
68. #10622279C22semidirect
69. #10622278C22semidirect
70. #10622278C22semidirect
86. C22×Q8×C11C23semidirect
141. C2×(C2×D11)⋊C4D4semidirect
150. C2×(C2×D11)⋊C4C23semidirect
151. C2×(C2×D11)⋊C4C23semidirect
152. C2×(C2×D11)⋊C4C23semidirect
153. C2×(C2×D11)⋊C4C23semidirect
155. C2×C4⋊Dic11C23semidirect
158. C2×Dic11⋊C4C23semidirect
159. C2×Dic11⋊C4C23semidirect
162. C2×C4×Dic11C23semidirect
163. C2×C4×Dic11C23semidirect
166. C11×#95C23semidirect
167. C11×#95C23semidirect
168. C11×#95C23semidirect
169. C11⋊#95C23semidirect
170. C11⋊#95C23semidirect
171. C11⋊#95C23semidirect
304. (C2×D11)⋊C4C2×D4semidirect
318. C2×#393D11semidirect
393. C22×D11#124semidirect
449. C23×Q8C2×D11semidirect
488. #393C2×D11semidirect
499. C2×#95C2×D11semidirect
500. C2×#95C2×D11semidirect
501. C2×#95C2×D11semidirect
548. C2×D11C2×#124semidirect
575. C22×Q8C22×D11semidirect
658. #95C22×D11semidirect
659. #95C22×D11semidirect
660. #95C22×D11semidirect
662. C2×C11#2472semidirect
810. C11C2×#2472semidirect
995. C2#13072745direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#670002
C22×#669992
C22×#669352
C22×C22⋊C4×D112
#130727452
C2×#106222882
C2×#106222852
C2×#106225742
C2×#106225702
C2×#106225582
C2×#106222832
C2×#106222782
C2×#106225682
C2×#106222792
C2×C11×#3932
C2×#247211